[tex]5\sqrt{2}=\sqrt{5^2*2}=\sqrt{25*2}=\sqrt{50}\\\\3\sqrt{5}=\sqrt{3^2*5}=\sqrt{9*5}=\sqrt{45}\\\\7\sqrt{3}=\sqrt{7^2* 3}=\sqrt{49*3}=\sqrt{147}\\\\2\sqrt{7}=\sqrt{2^2*7}=\sqrt{4*7}=\sqrt{28}\\\\\frac{2}{3}\sqrt{7}=\sqrt{(\frac{2}{3})^2*7}=\sqrt{\frac{4}{9}*7}=\sqrt{\frac{28}{9}}\\\\\frac{3}{5}\sqrt{5}=\sqrt{(\frac{3}{5})^2*5}=\sqrt{\frac{9}{\not{25}^5}*\not{5}^1}=\sqrt{\frac{9}{5}}[/tex]
[tex]\frac{1}{2}\sqrt{10}=\sqrt{(\frac{1}{2})^2*10}=\sqrt{\frac{1}{\not{4}^2}*\not{10}^5}=\sqrt{\frac{5}{2}}\\\\\frac{4}{7}\sqrt{14}=\sqrt{(\frac{4}{7})^2*14}=\sqrt{ \frac{16}{49} *14}=\sqrt{\frac{224}{49}}\\\\3\sqrt{\frac{2}{5}}=\sqrt{3^2*\frac{2}{5}}=\sqrt{9*\frac{2}{5}}=\sqrt{\frac{18}{5}}\\\\2\sqrt{\frac{2}{7}}=\sqrt{2^2*\frac{2}{7}}=\sqrt{4*\frac{2}{7}}=\sqrt{\frac{8}{7}}\\\\\frac{2}{3}\sqrt{\frac{3}{2}} =\sqrt{(\frac{2}{3})^2*\frac{3}{2}}=\sqrt{\frac{\not{4}^2}{\not{9}^3}*\frac{\not{3}^1}{\not{2}^1}}=\sqrt{\frac{2}{3}}\\\\\frac{1}{5}\sqrt{1,75}=\sqrt{(\frac{1}{5})^2*\frac{175}{100}}=\sqrt{\frac{1}{25}*\frac{7}{4}}=\sqrt{\frac{7}{100}}[/tex]
